Answer :
Answer:
g(1)=7 1/5
Step-by-step explanation:
vertex (-5,0) , y intercept(0,5)
the quadratic equation is in the form of a parabola: y=ax²+bx+c
y=a(x-h)²+k find a and b and c
5=a(0-(-5))²+0
5=a(5)²+0
5=25a ⇒ a=5/25 ⇒ a=1/5
-b/2a=h
-b=2ah ⇒=-b=2(1/5)(-5) ⇒ -b=-2⇒ b=2
y=c=5 ( when x=0, y intercept)
y=1/5x² + 2x + 5
g(1)=1/5(1)²+2(1)+5
g(1)=1/5+2+5
g(1)=7 1/5
A quadratic function has a degree of 2, and it is represented as: [tex]y = ax^2 + bx + c[/tex]. The value of g(1) is -7.2
Given that:
[tex](h,k) = (-5,0)[/tex] --- the vertex
[tex](x,y) = (0,-5)[/tex] --- the y-intercept
The quadratic function in vertex form is:
[tex]y = a(x - h)^2 + k[/tex]
Where:
[tex](h,k) = (-5,0)[/tex] --- the vertex
So, we have:
[tex]y = a(x - -5)^2 + 0[/tex]
[tex]y = a(x +5)^2[/tex]
Substitute [tex](x,y) = (0,-5)[/tex] to calculate the value of a
[tex]-5 = a(0 +5)^2[/tex]
[tex]-5 = a(5)^2[/tex]
[tex]-5 = a \times 25[/tex]
Divide both sides by 25
[tex]a = -\frac 15[/tex]
So, the quadratic equation is:
[tex]y = a(x +5)^2[/tex]
[tex]y = -\frac 15(x +5)^2[/tex]
Rewrite as a function
[tex]g(x) = -\frac 15(x +5)^2\\[/tex]
To calculate g(1), we simply substitute 1 for x
[tex]g(1) = -\frac 15(1 +5)^2[/tex]
[tex]g(1) = -\frac 15(6)^2[/tex]
[tex]g(1) = -\frac 15 \times 36[/tex]
[tex]g(1) = -7.2[/tex]
Hence:
The value of g(1) is -7.2
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